Practice Problems on the Navier-Stokes Equations ns 03 An incompressible, viscous fluid is placed between horizontal, infinite, parallel plates as is shown in the figure. The two plates move in opposite directions with constant velocities, Ur and Uz. The pressure gradient in the x direction is zero and the only body force is due to gravity which acts in the y-direction. 1. Derive an expression for the velocity distribution between the plates assuming laminar flow. 2. Determine the volumetric flow rate of the fluid between the plates. 3. Determine the magnitude of the shear stress the fluid exerts on the upper plate (at y-b) and clearly indicate its direction on a sketch. fluid with density, p, and dynamic viscosity, u U2

Show transcribed image textPractice Problems on the Navier-Stokes Equations ns 03 An incompressible, viscous fluid is placed between horizontal, infinite, parallel plates as is shown in the figure. The two plates move in opposite directions with constant velocities, Ur and Uz. The pressure gradient in the x direction is zero and the only body force is due to gravity which acts in the y-direction. 1. Derive an expression for the velocity distribution between the plates assuming laminar flow. 2. Determine the volumetric flow rate of the fluid between the plates. 3. Determine the magnitude of the shear stress the fluid exerts on the upper plate (at y-b) and clearly indicate its direction on a sketch. fluid with density, p, and dynamic viscosity, u U2